Solution to Endgame Corner

The first position is drawn although white has the better chances. Black has a weak pawn on g3 and also the bishop could become superior to the knight if the position opens up, since there are pawns on both sides of the board. In addition to this, black has to be careful that white king does not invade the queenside, via d5.

[Result "1/2-1/2"]
[FEN "8/3n2k1/5p2/2p1pP2/1pP1B3/1P3Pp1/4K1P1/8 w - - 0 1"]
[SetUp "1"]
1.Bc6 { White challenges the black knight. Black should think very carefully where the knight should go as its placement is the key factor in holding this position } Nb6$1
{ The best square for the knight is d6 where the pawn on f5 and e4 square are attacked simultaneously! Black plans to position the knight here, via c8. In the game my opponent played the weaker }
( 1...Nf8$2 2.Ke3 Nh7$6 3.Ke4 Kh6 4.Kd5 { and lost quite quickly, the knight is misplaced } )
( 1...Nb8$2 Bb5$1 { Is also bad for black since the bishop dominates the knight. White will either pick up the pawn on g3 or invade with his king via d5. In either case he will win the game. } )
2.f4 { My opponent and I spent some time after the game analysing this move. There are a couple of other options }
( 2.Ke3 Nc8 3.Ke4 Nd6 4.Kd5$2 Nxf5 5.Kxc5 Nh4 {is not what white wants!} )
(2.Bb7$5 { is interesting, keeping the knight out of play. Black can still hold the balance though, for example } Kh6 3.Ke3 Kg5 4.Ke4 Kh4 5.f4 exf4 6.Kxf4 Kh5$1 7.Kxg3 Kg5 8.Be4 Nc8 9.Kf3 Nd6 10.g4 Nxe4 11.Kxe4 Kxg4 12.Kd5 Kxf5 13.Kxc5 Ke5$10 { with a draw } )
2...exf4 3.Kf3 Kh6 4.Kxf4 Nc8 { this knight maneuver is just in time! }
5.Kxg3 Kg5 6.Be4 Nd6 7.Bd3 Nxf5$10 { with a drawn endgame. Exchanging doesn’t win for white and, now that black has activated his knight, he has no problems as the position has remained closed! }
1/2-1/2

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In the second position, black has an extra pawn. To win, black needs to find a way of advancing this pawn.

[Result "0-1"]
[FEN "8/8/7p/p2k2p1/P1p3P1/8/1PK5/8 b - - 0 1"]
[SetUp "1"]
1...Ke6$1
{ A neat winning move although moving the king to e5 would also do the trick. In the game I was short of time and having calculated that I was not winning the race to queen, I repeated moves }
(1...Kc5 2.Kc3 Kd5 3.Kc2 Kc5 { and a draw, was the game’s actual conclusion } )
( 1...Ke4$6 2.Kc3 Kf4 3.Kxc4 Kxg4 4.b4$1 { and white wins the race, but not the game } )
(1...h5$2 2.gxh5 g4 3.Kd2$1 Ke6 {doesn’t win, see below!} )
2.Kd2 {The best try, alternatively}
(2.Kc3 h5$1 3.gxh5 g4 { and black wins since white cannot capture on c4. Also after } 4.Kd4 Kf5 5.h6 Kg6 6.Ke4 Kxh6 7.Kf4 Kh5 {the pawn on g4 is defended. This was the critical variation that I missed during the game. })
(2.b4 cxb3 3.Kxb3 Kd5 4.Kc3 Kc5 5.Kb3 Kd4 {and the pawn on a4 will fall})
2...Kf6$1 {move order is important here}
(2...h5$2 {transposes to the variation considered above and throws away the win!} 3.gxh5 g4 4.Ke3 Kf5 5.h6$1 {and suddenly black is in trouble})
3.Ke3 Kg6 4.Kd4 {now that the king supports the breakthough, there is nothing better for white} 4...h5 5.gxh5 Kxh5 6.Kxc4 {black has won some valuable time and now wins the pawn race} 6...g4 7.Kd3 Kh4 8.b4 {too late!} 8...g3 9.Ke2 Kh3 {and the black pawn promotes!}
0-1